GeoGebra-5.04/C2/Theorems-in-GeoGebra/English

Visual Cue	Narration
Slide Number 1 Title slide	Welcome to the spoken tutorial on Theorems in GeoGebra.
Slide Number 2 Learning Objectives	In this tutorial we will state and prove, Pythagoras theorem and Midpoint theorem using Geogebra .
Slide Number 3 System Requirement	To record this tutorial, I am using; Ubuntu Linux OS version 16.04 GeoGebra version 5.0.438.0-d.
Slide Number 4 Pre-requisites www.spoken-tutorial.org	To follow this tutorial, learner should be familiar with GeoGebra interface. For the prerequisite GeoGebra tutorials, please visit this website.
Slide Number 5 Pythagoras Theorem The square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.	Let us state the Pythagoras theorem. The square of the hypotenuse is equal to the sum of the squares of the other two sides.
Cursor on the interface.	I have already opened the GeoGebra interface.
Cursor on the Graphics view.	We will begin with the drawing of a semicircle.
Click on Semicircle through 2 Points tool. Click two points in the Graphics view.	Click on the Semicircle through 2 Points tool. Then click to mark two points in the Graphics view.
Click on Point tool >> click on the semicircle c.	Using the Point we will mark another point C on the semicircle c.
Point to the semicircle c.	Let us now draw a triangle ABC using the points on the semicircle c.
Click on Polygon tool >> click points A, B, C and A again.	Click on the Polygon tool and draw triangle ABC on the semicircle. Here we are using semicircle to draw the triangle. This is because we need the measure of one angle to be 90 degree.
Point to the triangle.	Now let us measure the angles of the triangle ABC.
Click on Angle tool >> click inside the triangle	Click on the Angle tool and click inside the triangle. Here angle ACB is 90 degrees.
Point to Algebra view. Click on blue dot under Conic.	Now we will hide the semicircle c. In the Algebra view under Conic, click on the blue dot against c.
Point to the sides of the triangle.	We will draw three squares using the sides of the triangle.
Click on Regular Polygon tool >> click on the points C and B.	For that click on the Regular Polygon tool and then click on the points C, B.
Point to the dialog box and value 4. Click on OK button at the bottom.	The Regular Polygon text box opens with a default value 4. Click on OK button at the bottom.
Click on points B, C.	If you click on the points B, C, the square is drawn in the opposite direction.
Click on Undo button on the top right corner of the toolbar.	Let us undo the process by clicking on the Undo button.
Click on points A, C >> click button in Regular Polygon text box.	Now click on the points A, C. And then click the OK button in the text box that appears.
Click on points B, A >> click button in Regular Polygon text box.	Similarly click on the points B, A. And then click the OK button in the text box that appears.
Point to the three squares.	Now we have three squares that represent the Pythagorean triplets.
Click on Zoom Out tool >> click on the diagram.	Now we will use Zoom Out tool to see the diagram clearly.
Point to the three squares.	Now we will find the area of these squares.
Click on Area tool >> click on poly1 >> click on poly2 >> click on poly3. Point to the areas.	Click on the Area tool and click on poly1, poly2 and poly3 respectively. The areas of the respective squares are displayed.
Click on Move tool >> drag the labels.	Using the Move tool drag the labels to see them clearly.
Point to the areas of the squares.	Now we will check if the area of poly1 + area of poly 2 is equal to area of poly3.
In the input bar type poly1 + poly2 >> press Enter. Point to Algebra view.	In the input bar type poly1+ poly2 and press Enter. In the Algebra view a Number d, shows the value of area of poly3.
Point to the figure.	Hence Pythagoras theorem has been proved.
Point to the figure.	Now I will explain the Construction Protocol for pythagoras theorem. Construction Protocol shows the step by step construction of the diagram as an animation.
Click on View menu >> select Construction Protocol check box. Point to the view.	To view the animation, click on View menu and select Construction Protocol check box. Construction Protocol view opens next to Graphics view.
	I will drag the boundary of Graphics view view to see the Construction Protocol view.
Point to the columns in the table.	This view has a table with some columns. Below the table we have the animation controls.
Click on Play button. Point to the animation.	Now click on the Play button. Watch the step by step construction of the figure as an animation.
Slide Number 6 Mid point Theorem Line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it.	Next we will prove the Mid-point theorem. The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it.
Cursor on the interface.	I have opened a new GeoGebra window.
Click on Polygon tool >> click on the points A, B, C, D and A again.	Let us draw a triangle ABC using Polygon tool.
Point to the sides AB and AC.	Now we will find the mid-points of the sides AB and AC.
Click on the Midpoint or Center tool. Click on sides AB and AC.	Click on the Midpoint or Center tool. Then click on the sides AB and AC.
Click on Line tool >> click on points D and E.	Using the Line tool, draw a line through points D and E.
Point to the line AB.	Now we will draw a line parallel to segment AB.
Click on the Parallel Line tool >> click on segment AB. Click on point C. Point to the line.	For this, click on the Parallel Line tool and click on segment AB. Then, click on point C. Line g parallel to segment AB is drawn.
Point to the intersection point.	Notice that lines f and g intersect at a point.
Click on Intersect tool >> click on point of intersection.	Using the Intersect tool, let us mark the point of intersection as F.
Click on Angle tool >> click on the points F, C, E and D, A, E.	Now we need to measure angles F C E and D A E. Click on the Angle tool and click on the points F, C, E and D, A, E.
Point to the angles.	Notice that angles are equal since they are alternate interior angles.
Click on Angle tool >> click on the points C, B, D and E, D, A. Point to the line f and segment BC.	Similarly we will measure C, B, D and E, D, A . The angles are equal. It implies that line f is parallel to segment BC.
Click on Distance or Length tool >> click on points D, E and B, C. Point DE and BC.	Using the Distance or Length tool, click on the points D, E and B, C. Notice that DE is half of BC.
Point to the figure.	Hence the mid-point theorem is proved.
Point to the figure.	Once again I will show the Construction Protocol for the theorem.
Click on View menu >> select Construction Protocol check box. Point to the view.	Click on View menu and select Construction Protocol check box. Construction Protocol view opens next to Graphics view.
Click on Play button. Point to the animation.	Now click on the Play button. Watch the step by step construction of the figure.
Slide Number 7 Assignment In a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse.	As an assignment, prove this theorem.
Point to the figure.	Your completed assignment should look like this.
	Let us summarize what we have learnt.
Slide Number 8 summary	In this tutorial we stated and proved, Pythagoras theorem and Midpoint theorem using Geogebra
Slide Number 9 About Spoken Tutorial project	The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
Slide Number 10 Spoken Tutorial workshops	The Spoken Tutorial Project team conducts workshops and gives certificates. For more details, please write to us.
Slide Number 11 Forum for specific questions: Do you have questions in THIS Spoken Tutorial? Please visit this site Choose the minute and second where you have the question. Explain your question briefly Someone from our team will answer them.	Please post your timed queries in this forum.
Slide Number 12 Acknowledgement	Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.
	This is Madhuri Ganapathi from, IIT Bombay signing off. Thank you for watching.

Contributors and Content Editors

Madhurig, PoojaMoolya